Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 9x - 6$ and $ JT = 7x + 12$ Find $CT$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {9x - 6} = {7x + 12}$ Solve for $x$ $ 2x = 18$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 9({9}) - 6$ $ JT = 7({9}) + 12$ $ CJ = 81 - 6$ $ JT = 63 + 12$ $ CJ = 75$ $ JT = 75$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {75} + {75}$ $ CT = 150$